In this paper, the control of linear parameter-varying (LPV) systems with time-varying real uncertain parameters, where only some of the parameters are measured and available for feedback is considered. The control objectives are internal stability and disturbance attenuation in the sense of a bounded induced L/sub 2/-norm from the external disturbance to the controlled output of the system. Using parametric Lyapunov functions, the solvability conditions for dynamic output feedback controllers that depend on the measured parameters are expressed in terms of a set of linear matrix inequalities (LMI) and an additional coupling constraint which destroys the convexity of the overall problem. Hence, by transforming the coupling constraint into a rank condition, the problem is recast into a rank-minimization problem with LMI constraints. An algorithm based on the "alternating projections" method is proposed. Although the convergence of the algorithm is not guaranteed, an example is included that demonstrates the application of the results.